Self-pulsating nonlinear systems via dissipative parametric instability

The recently discovered dissipative parametric instability is presented in the framework of the universal complex Ginzburg-Landau equation. The pattern formation associated with the instability is discussed in connection to the relevant applications in nonlinear photonics especially as a new tool for pulsed lasers design.

Synthetic Polymer and Microbubble Systems for Gene Delivery to the Brain

Thesis (Ph.D.)--University of Washington, 2016-08

Effects of an asymmetric friction on the nonlinear equilibration of a baroclinic system

Following some recent linear and nonlinear studies the authors examine, using numerical simulations of a classical two-layer model, the effect of an asymmetric friction on the nonlinear equilibrium of moderately unstable baroclinic systems, The results show that the presence of an asymmetric friction leads to a significant wave scale selection: ''long'' waves (in terms of their zonal wavelengths) emerge with a traditional asymmetric friction (with the upper layer less viscous than the lower layer), while only ''short'' waves dominate with a nontraditional asymmetric friction (with the lower layer less viscous than the upper layer). The role of the nonlinear interactions and. more precisely, the effects of an asymmetric friction on the wave-mean flow and wave-wave interactions; and their consequences on the wave scale selection are examined.

Real-time load-side control of electric power systems

Two trends are emerging from modern electric power systems: the growth of renewable (e.g., solar and wind) generation, and the integration of information technologies and advanced power electronics. The former introduces large, rapid, and random fluctuations in power supply, demand, frequency, and voltage, which become a major challenge for real-time operation of power systems. The latter creates a tremendous number of controllable intelligent endpoints such as smart buildings and appliances, electric vehicles, energy storage devices, and power electronic devices that can sense, compute, communicate, and actuate. Most of these endpoints are distributed on the load side of power systems, in contrast to traditional control resources such as centralized bulk generators. This thesis focuses on controlling power systems in real time, using these load side resources. Specifically, it studies two problems.

(1) Distributed load-side frequency control: We establish a mathematical framework to design distributed frequency control algorithms for flexible electric loads. In this framework, we formulate a category of optimization problems, called optimal load control (OLC), to incorporate the goals of frequency control, such as balancing power supply and demand, restoring frequency to its nominal value, restoring inter-area power flows, etc., in a way that minimizes total disutility for the loads to participate in frequency control by deviating from their nominal power usage. By exploiting distributed algorithms to solve OLC and analyzing convergence of these algorithms, we design distributed load-side controllers and prove stability of closed-loop power systems governed by these controllers. This general framework is adapted and applied to different types of power systems described by different models, or to achieve different levels of control goals under different operation scenarios. We first consider a dynamically coherent power system which can be equivalently modeled with a single synchronous machine. We then extend our framework to a multi-machine power network, where we consider primary and secondary frequency controls, linear and nonlinear power flow models, and the interactions between generator dynamics and load control.

(2) Two-timescale voltage control: The voltage of a power distribution system must be maintained closely around its nominal value in real time, even in the presence of highly volatile power supply or demand. For this purpose, we jointly control two types of reactive power sources: a capacitor operating at a slow timescale, and a power electronic device, such as a smart inverter or a D-STATCOM, operating at a fast timescale. Their control actions are solved from optimal power flow problems at two timescales. Specifically, the slow-timescale problem is a chance-constrained optimization, which minimizes power loss and regulates the voltage at the current time instant while limiting the probability of future voltage violations due to stochastic changes in power supply or demand. This control framework forms the basis of an optimal sizing problem, which determines the installation capacities of the control devices by minimizing the sum of power loss and capital cost. We develop computationally efficient heuristics to solve the optimal sizing problem and implement real-time control. Numerical experiments show that the proposed sizing and control schemes significantly improve the reliability of voltage control with a moderate increase in cost.

Switching Patterns and Steady-State Analysis of Grid-Connected and Stand-Alone Single-Stage Boost-Inverters for PV Applications

Renewable or sustainable energy (SE) sources have attracted the attention of many countries because the power generated is environmentally friendly, and the sources are not subject to the instability of price and availability. This dissertation presents new trends in the DC-AC converters (inverters) used in renewable energy sources, particularly for photovoltaic (PV) energy systems. A review of the existing technologies is performed for both single-phase and three-phase systems, and the pros and cons of the best candidates are investigated. In many modern energy conversion systems, a DC voltage, which is provided from a SE source or energy storage device, must be boosted and converted to an AC voltage with a fixed amplitude and frequency. A novel switching pattern based on the concept of the conventional space-vector pulse-width-modulated (SVPWM) technique is developed for single-stage, boost-inverters using the topology of current source inverters (CSI). The six main switching states, and two zeros, with three switches conducting at any given instant in conventional SVPWM techniques are modified herein into three charging states and six discharging states with only two switches conducting at any given instant. The charging states are necessary in order to boost the DC input voltage. It is demonstrated that the CSI topology in conjunction with the developed switching pattern is capable of providing the required residential AC voltage from a low DC voltage of one PV panel at its rated power for both linear and nonlinear loads. In a micro-grid, the active and reactive power control and consequently voltage regulation is one of the main requirements. Therefore, the capability of the single-stage boost-inverter in controlling the active power and providing the reactive power is investigated. It is demonstrated that the injected active and reactive power can be independently controlled through two modulation indices introduced in the proposed switching algorithm. The system is capable of injecting a desirable level of reactive power, while the maximum power point tracking (MPPT) dictates the desirable active power. The developed switching pattern is experimentally verified through a laboratory scaled three-phase 200W boost-inverter for both grid-connected and stand-alone cases and the results are presented.

Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

Perceptions of fairness and allocation systems

This paper explores the conditions of acceptability of differing allocation systems under scarcity and evaluates what makes a price system more or less fair. We find that fairness in an allocation arrangement depend on the institutional settings inherent in the situation, such as information, transparency and competition and the perceived institutional quality e.g., fiscal exchange and institutional trust). Results also indicate that the solution “weak people first” is seen as the fairest approach to an excess demand situation, followed by “first come, first serve”, the price system and an auction system. On the other hand, a random procedure or an allocation through the government is not perceived to be fair. Moreover, economics students seemed to be less sceptical towards the price system than other subjects although we observe that female students are more sceptical than male students.